This work studied the infrared absorption of methane broadened by carbon dioxide, which can contribute to the radiative budget of CO₂-dominated atmospheres. Fourier transform absorption spectra of CH₄ perturbed by CO₂ were recorded in the 3.3 μm spectral region, at room temperature and total pressures ranging from 3 to 25 bars. These experimental data were modeled using a theoretical approach taking collision-induced line mixing into account. Comparisons between measured and calculated spectra demonstrate that the proposed model is capable of accurately representing the absorption of methane broadened by collisions with CO₂, from line centers to the far wings. For practical applications, this rigorous spectral modeling was used to derive a simple χ-factor model to represent the spectral shape of CO₂-broadened CH₄ line wings. Comparisons with experimental values show that, at room temperature, the proposed χ-factor reproduces the measured spectra to within 10% in the band wings where the absorption is mainly due to the far line wings, while the usual Lorentzian profile leads to relative differences several orders of magnitude larger. This line-shape correction was successfully validated through comparisons with heavily saturated spectra of the ν₃ band of methane recorded at sub-atmospheric pressures.